Instead of applying Newton's second law for the translation movement [itex] \frac{d\vec{\mbox{p}}}{dt}=\sum_{k} \vec{\mbox{F}}_{k} [/itex],try to apply it for the rotation movement [itex] \frac{d\vec{\mbox{L}}}{dt}=\sum_{k} \vec{\mbox{M}}_{k} [/itex]

where [itex]A[/itex] and [itex]\theta_0[/itex] are arbitrary constants. You can verify this by working out the second derivative and plugging it back into the differential equation. A general form of a sinusoidal function is

[tex]x = A \sin (\omega t + \theta_0)[/itex]

where [itex]\omega[/itex] is the angular frequency. Matching up the preceding two equations gives you